Differential equationsFind the indicate d partial derivative.
3 months ago
Find the indicate d partial derivative. f(x,y)=ysin^(-1)(xy); f_(y)(1,1/2)
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Best Answer
chancetherapperacidrapzip Staff answered 3 months ago
f(x,y)=ysin^(-1)xy Differentiate with respect to y, treat x like a constants f_(y)(x,y)=sin^(-1)xy+y*(1)/(sqrt(1-x^(2)y^(2)))*x f_(y)(x,y)=sin^(-1)xy+(xy)/(sqrt(1-x^(2)y^(2))) Therefore f_(y)(1, (1)/(2))=sin^(-1)(1)/(2)+((1)/(2))/(sqrt(1-(1)/(4))) f_(y)(1,(1)/(2))=(pi)/(6)+((1)/(2))/((sqrt(3))/(2)) f_(y)(1,(1)/(2))=(pi)/(6)+(1)/(sqrt(3)) Result: f_(y)(1,(1)/(2))=(pi)/(6)+(1)/(sqrt(3))
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